Golden Kebab Tokens

A group of Mad-Ade's friends, although fewer than 10, found a number of Golden kebab tokens which they were able to divide equally among them.

After this division had been done, Norha Bone - one of the friends, suggested that it would be more equitable to divide the Golden kebab tokens by families rather than by individuals. Among them, there were two groups with two sisters; of course Norha Bone was not in either group. The rest of the friends were unrelated to each other. A re-division by families would have meant that the Golden kebab tokens per family were 5 more than the Golden kebab tokens per friend.

The friends argued among themselves over this way of dividing the Golden kebab tokens. Before a final decision is made, Wendy Boatkumsin - one of the friends, decided that she did not want any Golden kebab tokens. Her share was equally divided (without breaking/cutting any Kebab token) among the other friends.

Finally, Norha Bone decided to withdraw her suggestion of dividing the Golden kebab tokens by families.

How many friends were there and how many Golden kebab tokens did each friend end up with?

Answer

There were a total of 6 friends. Each end up with 12 Golden kebab tokens.

The number of Golden kebab tokens is evenly divisible by the number of friends as well as the number of families.

Let's assume that N is the number of Golden kebab tokens each friend received initially and G is the total number of friends.

Then, total number of Golden kebab tokens = NG

If the Golden kebab tokens had been divided by families rather than by individuals, the number of recipients would be (G - 2) and each share would be (N + 5).
Again, total number of Golden kebab tokens = (N + 5)(G - 2)

Now, N and G are the positive integers and also total number of Golden kebab tokens must be divisible by G, (G-1) and (G-2). This is because initially there were G friends; then since it was divided family wise, the total number of units, the coins were to be divided would be (G-2) (as two groups had two sisters, so two friends got combined as one group, one per group); and after Wendy Boatkumsin backed out, there were (G-1) friends.

Now trying different EVEN values for G, starting with 2; there were total 6 friends and 60 Golden kebab tokens. The Golden kebab tokens are divided among 5 friends and hence each friend ends up with 12 Golden kebab tokens.Hide